Cooperation and the Emergence of Role Differentiat

arXiv:0712.1351v1[physics.soc-ph]9Dec2007Cooperationandemergenceofroledifferentiationinthedynamicsofsocialnetworks∗V´ıctorM.Egu´ıluzandMaxiSanMiguelInstitutoMediterr´aneodeEstudiosAvanzadosIMEDEA(CSIC-UIB),E07122PalmadeMallorca,Spain†Mart´ınG.ZimmermannFacultaddeCienciasExactasyNaturales,UniversidaddeBuenosAires,1428BuenosAires,ArgentinaCamiloJ.Cela-CondeDepartamentodeFilosof´ıa,UniversidaddelasIslasBaleares,E07122PalmadeMallorca,SpainBymeansofextensivecomputersimulations,theauthorsconsidertheentangledcoevolutionofactionsandsocialstructureinanewversionofaspatialPrisonersDilemmamodelthatnaturallygiveswaytoaprocessofsocialdifferentiation.Diversesocialrolesemergefromthedynamicsofthesystem:leadersareindividualsgettingalargepayoffwhoareimitatedbyaconsiderablefractionofthepopulation,conformistsareunsatisfiedcooperativeagentsthatkeepcooperating,andexploitersaredefectorswithapayofflargerthantheaverageoneobtainedbycooperators.Thedynamicsgenerateasocialnetworkthatcanhavethetopologyofasmallworldnetwork.Thenetworkhasastronghierarchicalstructureinwhichtheleadersplayanessentialroleinsustainingahighlycooperativestableregime.Butdisruptionsaffectingleadersproducesocialcrisesdescribedasdynamicalcascadesthatpropagatethroughthenetwork.I.INTRODUCTIONSocialtraps(Platt1973)aresituationsinwhichra-tionalindividualchoicesresultinanundesirablecollec-tiveoutcomeforthesocialgroup.Awellknownexam-pleistheproblemofestablishingcooperationinaso-cialgroup(Axelrod1994)or,moregenerally,problemsofpublicgoods(Olson1965,Hardin1968).Itisoftenrecognizedthattheunderstandingofcollectivesocialbe-havior,onceindividualattitudesareknown,requirestak-ingintoaccounttheinteractionsamongtheindividualsofthegroup,andthatthesearemediatedbyanetworkofsocialrelations(Granovetter1973,1978).Suchnet-workconstitutesthesocialstructureofthegroup.Theembeddednessoftheinteractionsinthesocialstructure(Granovetter1985)hasbeenidentifiedasamainingredi-entinexplainingtheevolutionofcooperation(MacyandSkvoretz1998).Itisalsowelldocumented(Lazer2001),thatinthesamewaythattheactionsoftheindividualsareaffectedbythesocialnetwork,thenetworkisnotanexogenousstructure,butitisrathercreatedbyindivid-ualchoices.However,therearenotmanyspecificmodelsofsocialdynamicsthatincorporateexplicitlytheconceptofco-evolutionofindividualandnetwork(Lazer2001).Infact,inthelongtermresearchagendaposedbyMacy(1991)acentralpointisthatthestructureofthenetworkshouldnotbeconsideredasgiven,butasavariable.Thequestionposedis...toexplorehowsocialstructuremightevolveintandemwiththecollectiveactionitmakespos-sible.Thisgoesfurtherbeyondmodelsinwhichthereis∗VMEandMSMacknowledgefinancialsupportfromMCyT(Spain)throughprojectsCONOCE;MGZthanksfinancialsupportfromFOMEC-UBAandCONICET(Argentina).†Electronicaddress:[e-mail]coupledfromtheevolutionoftheactionsoftheindividualsinthegroup.Inthecontextofreciprocalaltruismandthebuildingofcooperation,thisgeneralquestionwasimplicitlyconsideredwithinagametheorysimulationmodelnamedtheSocialEvolu-tionModel(SEM)(deVosetal.,2001;Zeggelinketal.,2000).Inthispaperweaddressexplicitlytheproblemofco-evolutioninaversionofthePrisoner’sDilemma(PD)(RapoportandChammah1965)inwhichplayersinteractthroughanetworkthatadaptstotheresultsofthegame,andthereforetotheactionsoftheplayers.Wefocusontheresultingtypeofsocialstructure(co-hesivegroupversussocialhierarchy),aswellasonthedynamicalmechanismsneededtoproducethetopologi-calpropertiesofthenetworkofinteractionsthatstabilizeacollectivecooperativebehavior.Amainresultofouranalysis,extensivelybasedoncomputersimulations(Zimmermannetal.2001),istheemergenceofaprocessofsocialdifferentiationtogetherwiththebuilding-upofanetworkwithhierarchicalrela-tions.Startingfromrandompartnershipamongequiv-alentindividuals,asocialstructureemerges.Inthisemergingstructure,thetopologyofthenetworkofsocialrelationsidentifiesindividualwithdifferentsocialroles:leaders,conformistsandexploiters.Theseroleshavebeenspontaneouslyselectedduringthecomplexadap-tiveevolutionofthesocialgroupthatentailsalearningprocess.Thissocialstructuresustainsglobalcoopera-tionwithexploiterssurvivinginhierarchicalchainsinthenetwork.Thisresultisatvariancewithothersim-ulationmodels,suchasSEM,inwhichpartnerselectionleadstotheformationofcohesiveegalitarianclusters(deVosetal.,2001;Zeggelinketal.,2000):theemer-genceofthesegroupsinasociallysegmentedpopulation,withexclusionoffreeriders,seemstobethebasisofthesurvivalofcooperationintheseotherstudies.Concern-ingthetopologyoftheco-evolvednetworkthatsustains2cooperation,wefindahierarchicalnetworkwithanexpo-nentialconnectivitydistribution.Ourresultsshowthatclusteringisnotneededtosustaincooperation.Howevertheadditionalinclusionoflocalneighboringpartnerse-lectioninthemodelgeneratesthecelebratedsmall-worldconnectivity(Watts1999)ofthenetwork.Fromaphilosophicalpointofview,theconceptofemergenceisusedincontemporarysociologyincon-tradictoryways,beingitspropermeaningdebatable(Sawyer2001).Weuseithereasitappearsinmulti-agentmodelsofsocialsystems(GilbertandConte1965;Schelling1978;